Local and global well-posedness of dispersion generalized Benjamin-Ono equations on the circle

Robert Schippa

doi:10.1016/j.na.2020.111777

paper

Local and global well-posedness of dispersion generalized Benjamin-Ono equations on the circle

arXiv:1906.01956 · doi:10.1016/j.na.2020.111777

Abstract

New local well-posedness results for dispersion generalized Benjamin-Ono equations on the torus are proved. The family of equations under consideration links the Benjamin-Ono and Korteweg-de Vries equation. For sufficiently high dispersion global well-posedness in $L^{2} (T)$ is derived.

38 pages